When we are constructing the Huffman tree to get the Huffman codes, Is it possible to give "1" to left side and "0" to right side rather than giving "0" to left side and "1" to right side of the tree?
You can assign the $1$ and $0$ as you like, but be consistent. Only your code change, i.e. a 1011 becomes a 0100.
Yes, You can.
But you'll need the Huffman tree to decode since the placing of left child and right child is arbitrary. If you're given an encoded string and ask you to decode, you can't do that since you don't know the exact algorithm which is used in building the Huffman Tree.